Related papers: Chain recurrent shifts on trees
We consider weighted shift operators having the property of moment infinite divisibility; that is, for any $p > 0$, the shift is subnormal when every weight (equivalently, every moment) is raised to the $p$-th power. By reconsidering…
Comparative and evolutive ecologists are interested in the distribution of quantitative traits among related species. The classical framework for these distributions consists of a random process running along the branches of a phylogenetic…
The one-dimensional fall of a folded chain with one end suspended from a rigid support and a chain falling from a resting heap on a table is studied. Because their Lagrangians contain no explicit time dependence, the falling chains are…
This work continues and substantially extends our recent work on switching diffusions with the switching processes that depend on the past states and that take values in a countable state space. That is, the discrete components of the…
We analyse the statistical properties of genealogical trees in a neutral model of a closed population with sexual reproduction and non-overlapping generations. By reconstructing the genealogy of an individual from the population evolution,…
We consider Reinforced Random Walks where transition probabilities are a function of the proportion of times the walk has traversed an edge. We give conditions for recurrence or transience. A phase transition is observed, similar to…
Begin continuous time random walks from every vertex of a graph and have particles coalesce when they collide. We use a duality relation with the voter model to prove the process is site recurrent on bounded degree graphs, and for…
We consider a continuous-time vertex reinforced jump process on a supercritical Galton-Watson tree. This process takes values in the set of vertices of the tree and jumps to a neighboring vertex with rate proportional to the local time at…
This work addresses the intrinsic relationship between trees and networks (i.e. graphs). A complete (invertible) mapping is presented which allows trees to be mapped into weighted graphs and then backmapped into the original tree without…
We consider multi-type Galton Watson trees, and find the distribution of these trees when conditioning on very general types of recursive events. It turns out that the conditioned tree is again a multi-type Galton Watson tree, possibly with…
It has been demonstrated that excitable media with a tree structure performed better than other network topologies, it is natural to consider neural networks defined on Cayley trees. The investigation of a symbolic space called tree-shift…
We get sharp estimates for the distribution function of nonnegative weights, which satisfy so called $A_{p_1, p_2}$ condition. For particular choices of parameters $p_1$, $p_2$ this condition becomes an $A_p$-condition or Reverse H\"{o}lder…
We consider a recurrent RWRE $(X_n)_{n \in \mathbb{N}_0}$ on $\mathbb{Z}$ and investigate the quenched return probabilities of the RWRE to the origin for which we state results on their decay in terms of summability. Additionally, we give…
We study the cyclicity in weighted $\ell^p(\mathbb{Z})$ spaces. For $p \geq 1$ and $\beta \geq 0$, let $\ell^p\_\beta(\mathbb{Z})$ be the space of sequences $u=(u\_n)\_{n\in \mathbb{Z}}$ such that $(u\_n |n|^{\beta})\in \ell^p(\mathbb{Z})…
Several real-world and abstract structures and systems are characterized by marked hierarchy to the point of being expressed as trees. Because the study of these entities often involves sampling (or discovering) the tree nodes in a specific…
The authors propose a new variation of random walks called ladder chains $L(r,s,p)$. We extend concepts such as ruin probability, hitting time, transience and recurrence of random walks to ladder chain. Take $L(2,2,p)$ for instance, we find…
An evolutionary tree is a cascade of bifurcations starting from a single common root, generating a growing set of daughter species as time goes by. Species here is a general denomination for biological species, spoken languages or any other…
In this paper we show that all infinite trees which have bounded coordination and whose surface is negligible with respect to the volume in the limit of large distances (so that they can be embedded in a finite-dimensional euclidean space)…
We prove that for recurrent, reversible graphs, the following conditions are equivalent: (a) existence and uniqueness of the potential kernel, (b) existence and uniqueness of harmonic measure from infinity, (c) a new anchored Harnack…
We introduce the Banach spaces $\ell^p_{a,b}$ and $c_{0,a,b}$, of analytic functions on the unit disc, having normalized Schauder bases consisting of polynomials of the form $f_n(z)=(a_n+b_nz)z^n, ~~n\geq0$, where $\{f_n\}$ is assumed to be…